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A295687 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 2, a(3) = 1. 1
1, 2, 2, 1, 4, 8, 11, 16, 28, 47, 74, 118, 193, 314, 506, 817, 1324, 2144, 3467, 5608, 9076, 14687, 23762, 38446, 62209, 100658, 162866, 263521, 426388, 689912, 1116299, 1806208, 2922508, 4728719, 7651226, 12379942, 20031169, 32411114, 52442282, 84853393 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth-rate of the Fibonacci numbers (A000045).

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, 1)

FORMULA

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 2, a(3) = 1.

G.f.: (-1 - x + 2 x^3)/(-1 + x + x^3 + x^4).

MATHEMATICA

LinearRecurrence[{1, 0, 1, 1}, {1, 2, 2, 1}, 100]

CROSSREFS

Cf. A001622, A000045.

Sequence in context: A304209 A137399 A158985 * A087854 A185041 A086873

Adjacent sequences:  A295684 A295685 A295686 * A295688 A295689 A295690

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 29 2017

STATUS

approved

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Last modified November 17 06:27 EST 2018. Contains 317275 sequences. (Running on oeis4.)